Registering a domain name only holds the address for you. So letting it lapse has nothing to do with whether all the 'stuff' on the website has been saved or not. That depends on who is hosting the website. You need to ask the host if they saved your information. Most likely they haven't unless you paid them to save the info.
A domain name and web storage are two different things. The web storage is where the contents of your website is held, the domain name is just used to point an address to this content. If a domain name expires it will not affect the contents of your website, it should still be saved on the server of your web host.